The present invention is applicable to the field of aircraft navigation systems. More particularly, when the demands on precision and integrity are greatest, in the approach and take-off phases, satellite navigation systems of the GNSS type (Global Navigation Satellite System, comprising the Global Positioning System constellations—GPS, GLONASS—Russian version of the GNSS—and in the future Galileo and Beidou, the future European and Chinese constellations; the invention would in fact be applicable to any satellite navigation system) are currently not able to guarantee the precisions and integrities required by the safety standards. Precision augmentation systems may be used such as GBAS (Ground Based Augmentation System) or SBAS (Satellite Based Augmentation System), but these systems are only available in areas that are specifically equipped. The present invention belongs to the family of ABAS (Airborne Based Augmentation Systems). Conventional hybridization techniques, based on a combination of inertial sensor measurements, such as gyrometers and accelerometers, with position, speed and attitude measurements extracted from the processing of the civilian codes transmitted by the satellites, are no longer adapted to these flight phases with severe demands on precision and integrity, notably because the errors in the positioning system are significantly affected in these flight phases by the errors due to propagation in the ionosphere and to the multiple pathways which indeed form the major parts of the measurement errors of the GNSS receiver in flight and on the ground, respectively.